The 16O+ 12C reaction at 90.5, 110 and 130 MeV beam energy

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Alma Mater Studiorum · Universit`

a di Bologna

Scuola di Scienze

Dipartimento di Fisica e Astronomia Corso di Laurea Magistrale in Fisica

The

16 O+

12 C reaction at 90.5, 110 and 130

MeV beam energy

Relatore:

Prof. Mauro Bruno

Correlatore:

Dott. Luca Morelli

Presentata da:

Catalin Frosin

Sessione III

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Abstract

Questo lavoro di tesi è inserito in uno studio, nell’ambito della collaborazione NUCL-EX, delle collisioni tra ioni pesanti per indagare le proprietà statistiche e la struttura della materia nucleare per sistemi con massa A<40. In particolare è stata studiata la reazione 16O+12C, ad energie di fascio di 90.5 MeV, 110 MeV e 130 MeV. Lo scopo della misura è quello di studiare il meccanismo di fusione-evaporazione e le possibili deviazioni da un decadimento puramente statistico del nucleo composto (28_Si∗_{) che si viene a}

for-mare. Il confronto tra i dati sperimentali e quelli ottenuti da una previsione basata sul modello statistico Hauser-Feschbach, ottimizzato per lo studio di nuclei leggeri (HF`), `

e in grado di fornire indicazioni su effetti di struttura come gi`a evidenziato in passato dalla collaborazione in reazioni analoghe. Questi sono principalmente legati nel nostro caso alla possibile struttura a cluster di particelle α che persistono oltre le soglie di emis-sione di particella. La misura `e stata effettuata presso i Laboratori Nazionali di Legnaro sfruttando il fascio fornito da un acceleratore Tandem XTU e l’apparato sperimentale

formato dai rivelatori GARFIELD e Ring Counter (RCo). L’analisi si `e concentrata

sia sullo studio di osservabili inclusivi come le distribuzioni energetiche e angolari delle particelle emesse che di osservabili esclusivi come la probabilit`a di decadimento in canali specifici. Questi risultati preliminari ottenuti per la reazione 16_O+12_{C hanno in effetti}

evidenziato la presenza di effetti di struttura legate all’emissione di cluster-α, in parti-colare quando il residuo `e un nucleo di carica pari. Si discute anche della dipendenza dall’energia incidente, e quindi dall’energia di eccitazione del 28_Si∗_{, di questi effetti.}

In conclusione si indicano gli aspetti da investigare con maggior dettaglio per ottenere risultati pi`u consolidati e cercare di definire le cause di queste deviazioni dal modello statistico.

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Introduction

The nuclear force at the nucleon scale is still one of the most active area of research in nuclear physics and many theoretical models have been developed throughout the years trying to reproduce at best the experimental data. In this framework, nuclear reactions with heavy ions are one of the main tools for investigating the structure and features of nuclear matter. They allow to access the excitation spectrum of the nuclei and to study their behavior in extreme conditions (temperature and/or density) far from their ground state. Furthermore, these states are of great interest for nuclear astrophysics studies as for example, stellar nucleosynthesis.

The NUCL-EX [1] collaboration in particular, has focused its attention on the study of the properties of light nuclei with atomic mass A<40 at low energies (below 20 AMeV). Both statistical decay of hot nuclei and nuclear clustering, as a deviation from the former mechanism, were investigated during the past experimental campaigns. A statistical de-cay code [11] developed by the collaboration (HF`), especially designed for light nuclei and containing the details of all the excited levels, has been used. The compound nucleus decay for fusion-evaporation reactions can be detailed and at the same time the param-eters of the HF` can be further constrained. The comparison between the model and experimental data, could evidence nuclear structure effects. Indeed, some excited states of even-Z nuclei in this mass region are known to present pronounced α-cluster effects even at high excitation energies. In this thesis, we want to study this physics case for the

16_O+12_{C reaction performed at three different beam energies (90.5, 110 and 130 MeV).}

In the case of complete fusion, this reaction, which employs α-cluster stable nuclei in the entrance channel, leads to the formation of a 28Si∗ system at respectively 55, 63 and 72 MeV excitation energy. From previous measurements on the decay of excited 24_{M g [32],}

cluster correlations are expected to persist also in the 28_{Si heavier system. Moreover,}

the three energies can point out how the cluster degree of freedom evolves varying the excitation energy of the system and leading to different decay patterns. In this cases, the observables of the reaction will show deviations from a statistical fusion-evaporation model. For example, one can study both global variables such as energy distributions or more exclusive ones as the Branching Ratio of particular decay channels.

To detect and identify the reaction products the GARFIELD and Ring Counter (RCo)

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together cover about 80% of the solid angle allowing to reconstruct on an event by event basis the single decay channels of the fused system when the whole charge of the reaction partners is collected. Both detectors employ the ∆E − E method and Pulse Shape Analysis (PSA) for identifying and measuring the energy of the incident particles. The results are then compared to the prediction of a HF` Monte-Carlo simulation.

This thesis is organized as follows. In Chapter 1 the general physics case of nuclear reactions will be introduced with particular attention to the complete fusion mechanism. For this type of reaction both the formation and statistical decay model will be described more in detail. In the last section, the cluster degree of freedom is presented along with a brief introduction to the previous results obtained by the NUCL-EX collaboration. Chapter 2 is dedicated to the characterization of the experimental apparatus which was employed for the current measurements, i.e. the GARFIELD+RCo detectors. In Chap-ter 3, we present the details of the reaction measurements and the main identification and calibration techniques for the decay products detected. As mentioned before, the results are compared to the HF` Monte-Carlo simulation which is summarised in Chapter 4. A more detailed description can be found in [11]. In Chapter 5 the first preliminary results for this reaction are shown and compared to the statistical model of the previous chapter. The observed deviations from the statistical model will be underlined and discussed in relation to clustering effects. Finally, conclusions and perspectives are drawn.

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Chapter 1 The Physics Case

Nuclei are finite quantum system and as such, they are characterized by their ground state and their excitation spectrum. The latter can be accessed by means of nuclear reac-tions. This implies that researches aiming at understanding the physics of excited nuclei heavily rely on the study of the reaction mechanisms themselves. These reactions allow observing the time evolution of the collision from a highly-out-of equilibrium situation (two cold colliding nuclei ) towards a possible thermalized system with high excitation energy and angular momentum. The stronger the nuclear excitation the larger becomes the number of quantum mechanical states which can be explored and consequently more nuclear properties far from the ground state can be studied.

Moreover, heavy ion collision can produce exotic and unstable new species (unusual neu-tron/proton ratio or superheavy elements) not found in nature, which can be further investigated.

In conclusion, the study of heavy-ion collisions is a powerful tool to investigate the physics of nuclear matter in extreme conditions of temperature and density. In this chapter, we describe the general physics framework related to the experiment described in this thesis, consisting of both a theoretical and an experimental introduction to the study and the decay of light nuclear systems.

1.1 Introduction to Heavy Ion Collisions

Heavy ion collisions can be classified according to some global ”topological” feature in order to separate and identify the ”sources” of the particles emitted and detected. These features are generally the impact parameter of the collision and the kinetic energy associated with the relative motion between the two partners of the collision. The former is defined as the distance between the asymptotic trajectory of the projectile and its parallel line passing through the centre of the target. The latter is the available centre-of-mass kinetic energy, transformed partially or entirely into excitation energy during

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CHAPTER 1. THE PHYSICS CASE

the interaction between the two colliding nuclei.

This dissipation process can be better understood by comparing the reduced relative wavelength of the initial partners in the reaction with the mean nucleon-nucleon distance in a nucleus (∼ 1.2 fm). The first parameter is given by:

ň = ~

mvaa

(1.1) where m is the nucleon mass and vaa is the relative velocity between the projectile and

target. If ň exceeds the mean nucleon-nucleon distance, then a collective behaviour of the nucleons during the collision can be assumed. In other words, the interaction be-tween nucleons inside the hot nuclear matter can be described via a mean field potential (one-body interaction). On the other hand, if ň is smaller than 1.2 fm a two body inter-action (nucleon-nucleon scattering) is used to explain the dissipation process. Therefore, according to eq. 1.1, the mean field effects prevail in the low-energy domain below 15 MeV/u incident energy, whereas two-body interaction start to become relevant above this value.

The different reaction mechanisms can also be easily classified using the impact pa-rameter ”b”, or alternatively the angular momentum ”l” (Figure 1.1). In fact, in a semiclassical approach they are related by:

b = lň (1.2)

Unlike the incident energy or the nuclei involved in the reaction, it is not possible to experimentally choose a priori the impact parameter. Estimates of ”b” are obtained by measuring variables monotonically correlated with it. An important value of ”b” is the one called the ”grazing” impact parameter (bgr); it represents the minimum value of ”b”

at which nuclear forces are negligible with respect to Coulomb interaction.

Based on the before-mentioned notions, we can identify four regions of different in-teraction mechanisms:

for l > lgr the projectile and the target nuclei interact only by means of the Coulomb

force. Therefore, the main processes are those of elastic or inelastic scattering. for lDIC < l < lgr the kinematics of the two nuclei is just slightly perturbed

as the nuclear force starts to grow. In this region (quasi-elastic) only external nucleons can interact while internal ones are not affected. These types of reaction are called Direct Reactions and it is possible to have few nucleons transfer between the projectile and the target.

for lcrit < l < lDIC (Deep Inelastic Scattering) the two partners re-separate after

a contact phase during which matter, angular momentum and significant amounts of energy are exchanged.

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Figure 1.1: Contribution to the differential cross section from the different reaction mechanisms as a function of the angular momentum.

for l < lcrit we are in the region of central collisions, where the dominant process

is the complete fusion of the reaction partners and the formation of a compound nucleus (CN). In Figure 1.1 the contributions of the various mechanisms to the cross section are shown. As it can be easily seen in some region different mechanisms overlap. The line dσ(l)_dl = 2πl_k2 shows the geometrical cross section.

In the following two subsections, we examine in more depth the various mechanisms and in particular we will focus on the formation of a compound nucleus.

1.1.1 Peripheral and Direct Reaction

Above and around the grazing value the main reaction mechanisms are elastic scat-tering or Direct and DIC collisions. In the first case, there is the possibility of having Coulomb excitation (or Coulex ). The Coulex mechanism is the transfer of energy to the target nucleus in the electromagnetic field of the projectile or viceversa. The excited nucleus then decays to its ground state by emitting γ-rays or few nucleons if it is excited above particle emission threshold. This process has been used for decades to obtain information related to low lying nuclear states [2, 3].

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In the second case, as we recall from the general description of nuclear reactions, a direct reaction occurs if one of the participants in the initial two-body interaction is transferred from one nucleus to the other. Generally speaking, these reactions are divided into two classes, the stripping reactions in which part of the incident projec-tile is transferred to the target nucleus and the pickup reactions in which the outgoing projectile-like particle is a combination of the incident nucleus and a few target nucleons. Typical stripping reactions are (d, p), (α, t) or (α, d) while common pickup reactions are (p, d), (p, t) and (α, 6_Li).

Going towards less peripheral collisions, the reacting nuclei acquire larger excitations and the nucleon exchange between them becomes more relevant. In fact, in deep elastic scattering, the colliding nuclei partially amalgamate (similar to a di-molecular state), exchange energy and mass and then re-separate under their mutual Coulomb repulsion. Therefore, in the exit channel, one normally detects a quasi-projectile fragment (QP) and a quasi-target (QT) with characteristics (mass and charge) that resemble the ones of the initial reaction partners. For semiperipheral collisions, DIC mechanism starts to compete with the formation of a compound nucleus.

1.1.2 Central Collisions and Compound Nucleus

Central collisions usually lead to the fusion of projectile and target nuclei. It is clear from Figure 1.1 that there is a critical angular momentum that separates fusion from the DIC region, even though this transition is not sharp but rather smooth with a small overlap around lcrit between the two distributions. Its value is governed by the

interaction potential between the interacting nuclei which consists of several terms: the Coulomb term that evolves as the inverse of the relative distance.

the nuclear force term which is negligible for large distances but becomes attractive when the relative distance is close to the sum of the nuclear radii. This contribution turns gradually into a repulsive force when the densities of the two nuclei significatly overlap.

the rotational contribution at finite impact parameter. This term is due to the combined effects of the angular momentum and moment of inertia of the system. In Figure 1.2 an example of the interaction potential evolution as a function of the relative distance is shown. To summarize, for l < lcrit a potential pocket exists which

traps the system inside due to the nuclear friction. In contrast, for angular momentum exceeding lcrit, the system is never trapped and the two partners separate after a contact

phase thus preventing the formation of a fused nucleus (CN).

The reaction process, in the case of fusion leading to a compound nucleus, can be divided into two steps well separated in time. The first step is the collision stage where

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Figure 1.2: The total interaction potential is shown for various values of l. The critical angular momentum corresponds to the l for which the pocket of the potential curve disappears [4].

the two nuclei merge and form a fully equilibrated excited nucleus on a time scale (about 10−21s) shorter than the following decay (from 10−19 to 10−16s). In fact, once the com-pound nucleus is created, it forgets the initial dynamics which has led to its formation except for the incident energy and angular momentum. This is called the Bohr’s inde-pendence hypothesis [5] and the cross section for the reaction:

a + A → C → b + B (1.3)

can be written as the product of two independent terms. The first one is the probability of forming the compound nucleus in the entrance channel ”i” (a+A) while the second is the probability that the CN decays in a given channel ”f ” (b+B), also called the Branching Ratio (BR):

σ_i→fE,J,π(CN )= σ_FCN(i)BRCN(f ) (1.4) To estimate the fusion cross section one can use, in a first approximation, a classical picture of the nuclear reaction [6]. In this simple picture, we can adopt the value ”bF”

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target (b < bF). Therefore, the total absorption cross section is simply given by:

σF =

Z bF

0

2πbdb = πb2_F (1.5)

Substituting in 1.5 the value of bgr we find the explicit energy dependence of the fusion

cross section: σF() = πR2 1 −B i (1.6) where R and B are the radius and the corresponding value of the interaction potential barrier, whereas i is the relative kinetic energy between projectile and target in the

centre-of-mass frame. An equivalent expression can be obtained in terms of the orbital

angular momentum, given eq. 1.2, where we attribute successive contribution to σF to

successive values of l. The cross section for a determined l can be thought as the area between circles with radii b = lň and b = (l + 1)ň, as shown in Figure 1.3.

Figure 1.3: The geometrical picture of the cross section for different given l values. As a result, the total absorption cross section σF can be written in terms of a sum over

angular momentum: σF = πň lcrit X l=0 (2l + 1) = πň(lcrit+ 1)2 (1.7)

A more efficient quantum extension of this classical formula for σF, can be derived

considering that, for some values of l, there will be finite probabilities for both scattering and absorption from the elastic channel. To account for these probabilities, we define a transmission coefficient Tl as the probability that a given partial wave l is absorbed. At

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this point, one can write instead of eq. 1.7 the following expression:

σF = πň lcrit

X

l=0

(2l + 1)Tl (1.8)

where now the semplification of a sharp cut-off, introduced at the beginning, is defined by:

Tl = 1 f or l < lcrit (1.9)

Tl = 0 f or l > lcrit (1.10)

Obviously, this picture is far from being complete since the formation of the CN can also be limited by many other conditions, such as the competition of non-compound processes accompanying fusion in the entrance channel. Nevertheless, eq. 1.8 provides a starting point which is needed in the derivation of the decay widths. Its general form will require additional consideration of the spin degree of freedom in the reaction and of the transmission coefficients Tl. Further details will be discussed with regard to the

Monte-Carlo implementation of the statistical model in chapter 4. In addition, as shown in Figure 1.1 and stressed in the beginning of this section, the transition at lcrit is not

sharp and therefore what is generally done is to consider a diffuseness around lcrit (bF),

to be taken into account in eq. 1.5, 1.7 and 1.8.

Concluding, we want to specify one last aspect on the compound nucleus formation cross section. The transmission coefficients introduced previously in eq. 1.8 are energy and momentum dependent, and thus related to the probability of creating the CN in a specific (discrete) state ”C”. As a consequence of this, resonances in the fusion cross section may appear. For a particular case of spinless projectile and target, the resonant CN formation cross section is given by:

σ_FC(i) = πň2(2l + 1) Γi_Γ (i− iR)2+Γ 2 4 (1.11)

where Γ and Γi are the total and the entrance channel ”i” decay widths, whereas i is

the relative kinetic energy between the collision partners in the entrance channel. After the CN formation, the system can decay either via evaporation or fission. For the reaction considered in this thesis (16O+12C), the former is the dominant decay process

while fission becomes relevant for heavier or highly deformed systems. Evaporation

means that the compound nucleus loses its excitation energy by emitting light charged particles (LCP) like p, d, t, 3He, α, 6,7Li, 8Be and neutrons. The remaining nuclear fragment, at the end of the decay chain, is called an Evaporation Residue (ER). The importance of resonances described earlier, in the decay of the CN source, is due to the fact that discrete levels can indeed be populated in daughter nuclei, which can further

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decay in products that keep memory of their ”resonant” origin. Decaying discrete states can then be reconstructed through particular techniques as correlation function in the relative momentum of coincident measured yields.

From an experimental point of view, the reaction mechanism is well understood if we are able to measure and identify the emitted particles, namely LCP and ER. However, one has to bear in mind that the final inclusive yields represent an integrated contribution over the whole time evolution of the decay chain. Because of that, the information they provide on specific energy regions of the different nuclei explored after the reaction may be model dependent. The challenge for an experimental measurement is to perform highly exclusive and complete detection of the decay products, in order to reconstruct their origin.

1.2 Statistical Decay

A compound nuclear system, even at the lowest incident energy at which fusion occurs, can explore many different configurations and decay in many different ways. This complexity is one of the justification for the use of a statistical model to describe the CN decay channels. In Section 1.1.2, we have described central collisions and in particular the formation of a compound nucleus. Hereafter, we will consider its decay and the statistical model used to explain the properties of the particles detected. This model is based on the assumption that all decay channel are equally likely and are governed by factors such as the density of the final state and barrier penetration factors.

The statistical model was first introduced and developed by several authors [5, 7, 8, 9], starting from late ’30s. A few years afterwards, Hauser and Feshbach [10] included a more extensive treatment of total angular momentum and this extended model became the foundation of the statistical decay models in use nowadays.

Considering a complete fusion, due to Bohr’s hypothesis, one can completely charac-terize the CN in terms of the charge ZCN, mass ACN and excitation energy E∗. These

values are simply given by charge/mass and energy conservation laws, related to Zp/Zt

and Ap/At of the reaction partners:

ACN = Ap+ At (1.12)

ZCN = Zp+ Zt (1.13)

E∗ = CM + Q (1.14)

where CM is the total kinetic energy of the system in the centre-of-mass frame and Q is

the Q-value of the reaction. For simplicity, in the following discussion, we will drop the subscript ”CN”. Therefore, given an excited nucleus of mass A, excitation energy E∗, charge Z and angular momentum J, we are interested in calculating the branching ratio (BRCN(f ) from eq. 1.4) of the different channels in which the system can decay. To do

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so, we need to evaluate the transition probability from an initial state ”i” to a final state ”f” given by Fermi’s Golden Rule [4]:

dNi→f

dt ∝ |Mi→f|

2

ρf (1.15)

where Mi→f represents the transition matrix and ρf is the final states density. As

already mentioned, the basic assumption of the statistical model is to consider that all transition matrix elements are equal so that only the density of the final states governs the transition probability. When applied to the case where the final state ”f” corresponds to the emission by a parent nucleus ”B” of a particle ”b” of spin ”s”, having a kinetic energy between and d, the evaporation probability per unit time for the process i → b + B becomes: Pb()d = C0ρf(Ef∗)dE ∗ f(2s + 1) 4πp2_dpV h3 (1.16)

This quantity is expressed as the product of three terms. The first one (C0) is a

normal-ization constant which is obtained from the detailed balance principle1_:

Pbρi(E∗) = Pf usρf(Ef∗) (1.17)

This means that the decay probability is linked to the reverse fusion reaction rate: Pf us=

vσF

V (1.18)

where σF is the fusion cross section of the particle ”b” with the final nucleus ”B” and

v is its velocity. The second term ρf(Ef∗)dE ∗

f is the number of states available for the

excited daughter nucleus and lastly, 4πp_h23dpV indicates the number of states of the emitted

particle with linear momentum between p and p + dp. When evaluating these three terms of eq. 1.16, one finally obtains:

Pb()d = ρf(Ef∗) ρi(E∗) (2s + 1)4πp 2 h3 σF()d (1.19)

As a consequence of eq. 1.19, a de-excitation channel will be more favourite if the number of accessible states (ρf) is large, emphasizing the role played by the density of states.

For a more detailed understanding of the emitted particle energy distribution, it is necessary to express the ingredients of this equation. In particular, we have to specify the densities of states for a nucleus with excitation energy between E∗ and (E∗+ ∆E∗)

1_{the detailed balance principle assumes that microscopic phenomena are time reversal invariant.}

Therefore, the transition probability of a system from state ”i” to ”f” is related to the probability of the inverse transition.

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and the fusion cross section. The former can be related, in a microcanonical approach [4], to the entropy2 _{S of the system and to its temperature:}

S = ln(ρ(E∗)∆E∗) (1.20) 1 T = dS dE∗ ≈ ∆lnρ(E∗) ∆E∗ (1.21)

Hence, the density of states exhibits an exponential evolution with the excitation energy:

ρ(E∗) ∝ eE∗/T (1.22)

This exponential increase in ρ(E∗) means that for high enough energies the different states form a continuum in which is impossible to separate one level from another, validating once more the use of a statistical approach. The fusion cross section instead may be written by means of eq. 1.6 as it follows:

σF() = πR2 1 − B Coul b (1.23) for ≥ BCoul

b and zero otherwise. Here BbCoul stands for the Coulomb barrier associated

with the emission of a particle ”b”. All these set of equations previously described lead to the final form for the emission probability Pb() (normalized to unity):

Pb() = − BCoul b T2 e −(−BCoul b )/T (1.24)

where the excitation energy E_f∗ is expressed as a function of the kinetic energy : E_f∗ = E_{f max}∗ − . The temperature ”T” in eq. 1.24 is the temperature of the final nucleus. From eq. 1.24, one can notice that the emission Pb(), thus also the energy distribution,

follows a Maxwellian distribution typical of the decay of an equilibrated nucleus.

The previous discussion can be extended to include the whole decay chain of a CN, i.e. one can picture the decay to the final state as a sequence of single particle emissions. In this case, ”T” represents the mean temperature as every evaporated particle leaves the CN in a new state with an excitation energy less than the initial nucleus. Therefore, the final Maxwellian spectrum is given by the sum of the single evaporation steps. At the end of the evaporation chain, when the daughter’s excitation energy is below the particle emission threshold, the ER de-excites by γ-rays emission. An illustrative picture of a fusion-evaporation chain is shown in Figure 1.4. The competition between various channels, i.e. the emission probability for different particles may be obtained from the integration of eq. 1.24 before normalization. Without going into the details of this

2_{Here we have assumed the Boltzmann constant (k}

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Figure 1.4: Picture of a fusion-evaporation reaction and the following compound nucleus decay.[11].

derivation, the total emission probability for a given particle ”b” is mainly influenced by the final state of the daughter nucleus:

Pb ∝ ρf(Ef∗− Q − B Coul

b ) (1.25)

The statistical model of Hauser-Feshbach, as stated at the beginning, extends this simple model be including a summation over the total angular momentum in the integration of the emission probability. The complete formula for the decay probability used to calculate the branching ratio, will be shown and discussed later on in chapter 4.

The Monte-Carlo implementation (HFl ) of the Hauser-Feshbach statistical decay model, was developed within the NUCL-EX collaboration and a detailed description of it is given in ref.[11]. This model in particular was adapted for low mass nuclei (A<40) and all the experimental results obtained are compared with the simulated data filtered with the detector response. In this way we can account for the detector’s geometry and angular resolution, as well as the energy thresholds and resolution of the individual detectors.

1.3 Structure and Clustering Effects

One of the goals of nuclear reactions is to infer the nuclear structure of the systems formed in the collisions by detecting their decay products. Therefore, one tries to under-stand the behaviour of protons and neutrons in the nucleus and the force that governs their interaction. Historically, from a theoretical point of view, the first successful model which was introduced was the shell model, which was able to define particular stable nuclei configurations based only on an independent particle approximation. This model

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explained many important properties of the nucleus such as the binding energy in the ground state, the proton and neutron separation energy and the so called ”magic num-bers”, i.e. the closed shell of neutrons and protons, respectively [12]. Unfortunately, this model could not explain the existence of many other nuclear levels experimentally seen in nuclear collisions. The aforementioned levels were attributed to a correlation between nucleons and to collective excitations of the nuclear system. In order to take these effects into account, new and more complex models were developed, namely the ”rotational” and ”vibrational” models.

Besides the interest in nucleon-nucleon correlation, another great challenge is the understanding of cluster-cluster (for example α-clustering) correlation, especially in light nuclei with N=Z. These new degrees of freedom, therefore, are now included in the new models predicting the nuclear structure. In the last decades, this arguments become of great appeal from both experimental and theoretical perspectives as indicated by the work of many authors [13, 14, 15, 16, 17]. As a result, starting from the ’60s, a campaign of measurements began to search for resonant structure in the excitation function for various combinations of light N=Z nuclei in the energy regime from the Coulomb barrier up to regions with excitation energies of E∗ = 20 − 50 MeV. Different types of clustering behaviour were identified in nuclei (see Figure 1.5), from small clusters outside closed shells, to complete condensation into α-particles, to halo nucleons outside of normal core.

Figure 1.5: Variety of types of nuclear clustering [18].

In light alpha-conjugate nuclei, clustering is observed as a general phenomenon at high excitation energy close to the alpha-decay thresholds. This exotic behaviour is well illustrated in the ”Ikeda-diagram” for N=Z nuclei [19], which has been modified and extended by von Oertzen [20] for neutron-rich nuclei, as shown in Figure 1.6. For

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Figure 1.6: Extended Ikeda-diagram with alpha-particles (left), 16O-cores (middle) and

14_{C-cores (left) [20]. The numbers represent the threshold energy (in MeV) dissociating}

the ground state into the respective cluster configuration.

example, in the bottom left side of Figure 1.6, the16O nucleus at excitation energy above 14.44 MeV can be sketched as a system formed by 4-α particles. The unstable ground state of8_{Be is maybe the most simple and convincing example of alfa clustering in light}

nuclei and it is well known to decay into two α particles with a half-life of 2.6· 10−6s. Moreover, clusterization is intimately connected with the formation of elements and even life itself. These two aspects intersect in 12_{C and the Hoyle-state. This excited}

state (7.65 MeV) of12C was proposed by Sir Fred Hoyle more than 50 years ago [21] and represents the gateway through which carbon is synthesized in stars via what is known as the triple-alpha process:

α + α + α →8 Be + α →12C∗ [Jπ = 0+, 7.65M eV ] (1.26)

Its actual structure in terms of alpha-particle components has been described in various ways, from a linear α-chain [22] , to a Bose-Einstein condensate or a diluite alpha-particle gas [23]. Still, the structure of the Hoyle state remains controversial as experimental results in favour of one or another hypothesis are found to be in disagreemet [24, 25]. It is an argument of debate whether the decay mechanism is sequential, through the formation

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of8_Be

gs, or if the simultaneous decay in three α-particles can play a significant role in the

decay of the Hoyle state. The results mentioned in [25, 26, 27], all indicate the former as the dominant process with a very low limit to the possible contribution from the latter process. On the contrary, the authors in [24] have measured, in a reaction with heavier systems than the aforementioned results, a few percent contribution of the simultaneous decay to the total decay mechanism of the Hoyle state. Further measurements are needed in order to investigate if a large nuclear medium, as in the second case, can affect the decay mechanism of this Carbon excited state.

1.3.1 The

16

O nucleus

Similarly to the 12_{C, a quest for 4-α or carbon-core based cluster states in} 16_{O, as in}

Figure 1.6, has started. In particular, these state can be detected near the8_Be+8_{Be and} 12_{C + α decay thresholds. In 1967 Chevalier et al. [28] could excite these states in an}

alpha-particle transfer channel leading to the8_Be+8_{Be final state. They then proposed}

that a structure corresponding to a rigidly rotating linear arrangement of four alpha particles may exist in16O. The8Be+8Be decay has also been studied in a measurement of the12_C(16_{O, 4α)}12_{C by Freer et al. [29]. Despite the fact that many of the states found}

in the excitation spectrum by Freer et al., and other more recent works [30], coincide with the ones found by Chevalier et al., the current results do not provide enough evidence to confirm the proposed linear chain of four α-particles.

More recently, in the case of a12_{C core, a new state with the structure of a Hoyle state}

coupled to an alpha particle was predicted in 16O at about 15.1 MeV [31]. The energy

of this state is just 700 keV above the 4-α breakup threshold, therefore it is expected to decay mainly by alpha emission to the Hoyle state with very small gamma decay branches. From a theoretical point of view, this was interpreted by [31] as a signature of Bose-Einstein condensation. To confirm this hypothesis, the 16_{O excitation spectrum}

must be measured with very efficient coincident particle detection which allows to have a good background rejection and to clearly separate the levels of interest.

1.4 The

16

O+

12

C Reaction

The aim of the experiment performed and analyzed during the work for this thesis is to progress in the understanding of statistical properties of light nuclei as well as studying new α-cluster states at excitation energies above particle emission thresholds. By using an exclusive channel selection and a highly constrained statistical code, one is able to put in evidence deviations from a statistical behaviour in the decay of hot fused nuclei formed in heavy-ion collisions. Moreover, one can also select a reaction leading to the excited projectile-like nucleus formed in a non-central collision and study the decay of this system. This is one of the methods used in literature to study the

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Hoyle state cluster structure, as described in section 1.3, and that of many other nuclei as well. Hence, given this reaction, one is capable of performing both statistical decay and particle spectroscopy experimental studies.

The reactions, 16_O+12_{C at 90.5, 110 and 130 MeV incident energy, have been}

inves-tigated within the campaign started by the NUCL-EX collaboration. The goal was to study the physics case previously described in this chapter. The results obtained in the past by the collaboration suggested a possible alpha-structure correlation in the 24_{M g}

compound nucleus formed in two different reactions (12_{C +}12_{C at 95 MeV and}14_{N +}10_B

at 80.7 MeV) but populated at the same excitation energy [32]. The reactions were per-formed in order to study if an influence of the entrance channel is present, by specifically using reaction partners with (12_{C +}12 _{C) and without (}14_{N +}10 _{B) a definite cluster}

structure. The experiments used the same GARFIELD + RCo apparatus to detect the reaction products. A general description of the detector is given in Chapter 2.

The analysis focused on the selection of fusion-evaporation channel mechanism, based on the coincidence between LCP’s (GARFIELD) and an evaporation residue (RCo) in complete events (total detection of the charge). A first hint for a possible contamination from α-structure correlation came from the comparison between energy spectra, from protons and α particles detected in GARFIELD in coincidence with different residue,

and a Hauser-Feshbach statistical model as shown in Figure 1.7. For the 12_{C +}12 _C

Figure 1.7: Proton (upper part) and α (lower part) energy spectra in complete Zdet=12

events detected in coincide with a Zres charge residue, for the 12C +12C reaction at 95

MeV incident energy. The black dots indicate the experimental measurements while the red lines are the model predictions [32].

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reaction, this figure shows a very good agreement between the data and the model for the proton energy spectra while the same cannot be stated for the α-particles detected in coincidence with an Oxygen fragment. In particular, in the O + 2α channel a much higher experimental branching ratio with respect to the model was evinced [32].

The experiment of this thesis is a natural extension of the aforementioned studies as the cluster correlation previously observed in the decay of the excited 24M g nucleus could possibly be present also in the 28_{Si at higher excitation energies. Furthermore,}

due to the three different beam energies, one could also investigate the evolution of the clustering degree of freedom varying the excitation energy of the system, as recently done by Vadas et al. [33].

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Chapter 2 The Experimental Apparatus

In nuclear heavy ion reactions, one has to detect a very large number of different particles, from protons to fission fragments, in a wide range of energy which can vary from tens of kev to GeV. These are very important to study the behaviour of a nuclear system undergoing a reaction. For instance, in the case of a compound nucleus, any change in its nuclear matter characteristics such as pressure, density or isospin, can be correlated to the variation of experimental signatures directly obtained from the detected products .

More in general, to efficiently measure, disentangle and weight all decay channels of an excited system formed in a collision, it is necessary to detect and identify all the reaction products. Thus the use of G.AR.F.I.E.L.D (General ARray for Fragment Identification and for Emitted Light particles) detector, coupled with Ring Counter (RCo) and installed at LNL-INFN [34], is very well suited for such measurements. Using these two detectors allows having for every event nearly complete information on light charged particles and more heavier mass fragments.

The coupled system covers nearly 4π of the total angle with high granularity, low energy thresholds, large dynamic ranges in energies and identification capabilities on an event by event basis. These characteristics are fundamental for a complete reconstruction of the kinematics for each event.

In the following sections, we briefly describe the main features and working principles of the experimental apparatus used to perform the experiment.

2.1 GARFIELD Apparatus

GARFIELD is a multi-detector consisting of two large-volume drift chambers, C1 and C2 (Figure 2.1), placed back to back with respect to the target. The detector is equipped with digital electronics and it is mainly based on ∆E-E telescopes. These telescopes exploit energy measurements in two different stages of the detector to obtain

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CHAPTER 2. THE EXPERIMENTAL APPARATUS

charge identification and accurate energy measurements of the reaction products. The forward chamber (C2) has cylindrical symmetry with respect to the beam axis and it is mechanically divided into 24 azimuthal sectors. Each sector has four CsI(Tl) crystals covering the polar angular region between 29.5°< θ < 82.5°, plus a micro-strip gas chamber pad (MSGC ) that is used as the first stage of detection (∆E stage), whereas the CsI(Tl) crystals measure the residual energy of particles (E stage). Overall, the forward chamber consists of 96 ∆E(gas)-E(CsI(Tl)) modules. The scintillators have different

Figure 2.1: Trasverse view of the GARFIELD Appartus coupled with the RCo. shape and dimensions as to adapt better to the polar angle θ (Table 2.1). Furthermore, they are placed in such a way that impinging particles coming from the target enter perpendicularly to the crystal face in its center (Figure 2.2).

CsI-1 CsI-2 CsI-3 CsI-4 CsI-5 CsI-6 CsI-7 CsI-8

θmin 139.9° 127.5° 113.5° 97.5° 68.0° 53.0° 41.0° 29.5°

θc 145.2° 133.0° 120.0° 104.8° 75.3° 60.0° 47.0° 34.9°

θmax 150.4° 138.5° 126.5° 112.0° 82.5° 66.0° 52.0° 40.0°

Table 2.1: Minimum, central and maximum angles corresponding to the regions covered by each GARFIELD CsI(Tl) crystal.

The backward chamber (C1) covers the region 97.5°< θ < 150.4°. This drift chamber has a structure very similar to C2 except for the fact that three sectors are missing, reducing the total coverage in φ. Nevertheless, a total active solid angle of 7.8 sr is

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covered by the two chambers. The intent of this design is to allow for future mounting of other possible detectors like the ones studied by the FAZIA collaboration [35].

Figure 2.2: Lateral view of one of Garfiled’s sectors.

Granularity is obtained by dividing each GARFIELD drift chamber in sectors with

an angular width of ∆φ = 15°. An even greater granularity is then achieved by taking

advantage of the fact that the microstrip pads are further divided in the azimuthal coordinate. This characteristic is well illustrated in Figure 2.3. All in all, the apparatus

can reach angular resolutions of ∆φ = 7.5° and ∆θ = 14° if the chambers are used as

ionization chambers. The azimuthal resolution is increased to about 1° if also the drift time is used.

The two drift chambers are filled with flowing CF4 (carbon tetrafluoride) gas at a

pressure around 50 mbar for C2 and around 20 mbar for C1. In the latter case, the adopted pressure is lower since the only backward detected particle are protons and alpha. Therefore, only the PSA technique with the CsI(Tl) is employed and the lower pressure allows having lower identification thresholds. Even so, a minimum value of 20 mbar has to be used as to cool down the preamplifier electronics located inside the chamber. The employed CF4 is a stable gas and it is suitable for detectors due to its

high stopping power (five times larger than CH4 and 17 % more than isobuthane), high

density (3.93 mg/cm3 at STP) and relatively low cost. Its average ionizing potential is around 16 eV and it has a high drift velocity (about 10 cm/µs at 1 V /cm · T orr). This being said, the charge produced is usually collected within 2-3 µs.

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2.1.1 Drift Chamber and Microstrip

The particles produced in a reaction, after passing through the entrance window, enter into the drift chambers where they interact with the gas. This interaction is due to the Coulomb force (electromagnetic interaction) and can cause either excitation or ionization of the gas molecules. It is this second process that generates the electron-ion pairs which represent the charge carriers. These carriers are afterwards collected by the electrodes due to the drift field created inside the gas volume.

The GARFIELD chambers have a 6 µm thick (0.78 mg/cm2) mylar entrance window

with thin metallic deposited strips. This thickness keeps low the window dead layer while maintaining a safe mechanical robustness to sustain the pressure deformations. The gas circulates in a closed circuit system and it is forced to flow in a continuous cycle (the time required for a total replacement is of the order of minutes). This is necessary for the purpose of eliminating any impurity or contamination such as molecules produced by the CF4 breaking or oxygen and water vapor infiltrations.

Inside the drift chamber a drift cathode at around -1000 V and a Frisch grid (at 60 V) generate an electrical field oriented in such way that the electrons formed along the trajectory of the particles are forced to drift toward the microstrip pads (see Figure 2.2). Due to the geometry of the sector, the cathode is made by many strips kept at the proper voltages via a resistive divider to make the electric field as homogeneous as possible. For the same reason, a series of additional electrodes are used at different potential via resistive dividers (scaled taking into account the irregular shape of the chamber) also on the front and side surfaces of the various CsI crystals and on the entrance window. These electrodes contribute to maintain the electric field uniform so that electrons move with constant drift velocity. Typical values of electric field inside the GARFIELD chamber are of the order of 104 _V/m.

The Frisch grid separates the region close to the microstrips, in which the electric field reaches a much greater intensity and sufficient to start the multiplication effect (avalanche effect), from the region where the electrons simply drift towards the electrodes. Moreover, it prevents the induction of signals on the microstrips when charge carriers drift in the active gas volume and it eliminates the positive ions contribution to the signals.

The microstrip pads (Figure 2.3) have a trapezoidal shape (with dimensions of ap-proximately 4 cm for the larger base, 2 cm for the smaller base and 7 cm for the height) and they are placed almost perpendicular to the beam axis. Each pad is divided into four charge collection zones, indicated conventionally with ul, ur, dl and dr. The letters u, d, l and r stand for up, down, left and right when one looks at the glass pads with the small base downward. Therefore, the two down areas are those closest to the beam, while the two up are the furthest. The division of each pad allows having four indipendent regions of signal collection, hence providing ∆E values to use for ∆E − E correlations. The cathodes are generally grounded whereas the anodes are connected to a certain bias voltage which allows the device to operate in a proportional mode. Therefore, the

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num-CHAPTER 2. THE EXPERIMENTAL APPARATUS

ber of collected electrons and the output signal are proportional to the energy deposited by the incident particle.

Figure 2.3: Microstrip geometry and division in the four electrically separated regions of signal collection.

The choice of using microstrip gas as detectors was influenced by two important requests. First of all, it is necessary to keep the identification energy threshold as low as possible (around 0.8-1 MeV/A) and secondly, they still have to be able to detect particles with a wide range of energies. Furthermore, MSGC have the advantage of a high signal-to-noise ratio for low ionization ions. In fact, microstrip chambers can sustain high counting rate and high gains (gain factor varying from 30 to 50 ) and they are nevertheless drift chamber which makes it possible the measurement of the particle position .

2.1.2 CsI(Tl) Crystals

As mentioned in the previous section, the GARFIELD apparatus uses mainly ∆E −E modules to detect and identify the incident particles. After the first ∆E part, for the last stage of detection a detector that can stop and efficiently measure the reaction products that pass through the gas volume is needed. Therefore, CsI(Tl) crystals have been chosen due to their excellent characteristics, like the high stopping power, the sufficiently good energy resolution (close to 3%-4% with 5.5 MeV α particles from241Am source [36]), the small sensitivity to the radiation damage and the fact that they are quite easy to cut and machine in order to obtain the shape needed for the experiment. These crystals in particular, have variable thicknesses of about 3–4 cm and different shapes depending on

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the θ angle, as already mentioned in section 1.1 . The different shapes of GARFIELD CsI(Tl) crystals are illustrated in Figure 2.4.

Figure 2.4: Shape of GARFIELD CsI(Tl) crystals. The A shape corresponds to the nearest to the microstrip plane (θ greater with respect to the beam line).

Another advantage of CsI(Tl) detectors is the possibility to perform pulse shape analysis (PSA) for detected particles. As a matter of fact, the scintillation of the CsI(Tl) crystal is well described by the sum of two exponentials with different time constants: a short one (τs ∼ 0.75µs ) and a long one (τl ∼ 5µs). As a result, the current pulse

produced in the photodiode by the scintillation light is described by: il(t) = dQL(t) dt = Qs τs e−τst + Ql τl e−τlt _(2.1)

where QL(t) is the whole collected charge at time t; Qs and Ql are the charges produced

respectively by short and long components of scintillation. QL is thus given by:

QL =

Z ∞

0

dQL(t)

dt = Qs+ Ql (2.2)

Particle identification capability comes from the different charge and mass dependence of Qs and Ql components. Also τs and τl values slightly depend on charge and mass of

the particle. In general, with the same total charge, the short component grows when Z increases.

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Concerning their stopping properties, these crystals are able to stop protons and α-particles with energies up to ∼100 MeV/u. Each crystal is wrapped in a white diffusive paper to maximize the collection of light and finally protected with an opaque layer to avoid light penetration from outside. This is to be considered as an additional 1.5µm thick dead layer when reconstructing the original energy of particles from the residual energy. The rear part of the crystal is tapered to behave as a light guide and it narrows to reach the dimensions of the photodiode coupled to the crystal. This photodiode is the model S3204-05 manufactured by Hamamatsu, with an active area of 18 mm x 18 mm. The choice of using photodiodes instead of photomultiplier tubes is due to their greater stability, low power dissipation, much smaller size and to their low bias voltage (∼ 100V ) which makes possible the operation inside the GARFIELD low pressure gas chamber.

2.2 Ring Counter

The Ring Counter (RCo) is an annular detector designed to be centered at 0° with

respect to the beam direction. It is an array of three-stage telescopes realized in a truncated cone shape. The first stage is an ionization chamber (IC), followed by a strip silicon detector (Si) while the last stage is formed by CsI(Tl) scintillators. The RCo uses PSA and the ∆E − E telescope techniques to identify and detect particles.

Each stage of the RCo is mounted on a low-mass aluminum support that is adjustable, for the relative alignment of all the active elements of the device. The preamplifiers are mounted on the same sliding plate of the RCo. A picture of the whole apparatus is shown in Figure 2.5.

During the measurement, the Ring Counter is inserted just in the forward cone of the GARFIELD metallic cage and its entrance window is placed 170 mm far from the target. The detector covers the polar angles in the range 5.4°< θ < 17.0°. The Ring Counter has a cylindrical symmetry along the beam axis and it is divided into 8 azimuthal sectors. Each sector thus covers 45° in φ (azimuthal coordinate).

The IC is a 6 cm long axial type chamber with the electric field parallel to the ion tracks in the gas. The field inside the IC is generated by three aluminized mylar electrodes. There are two input-output electrodes which are the grounded cathodes, while the anode is a central foil with metal deposition on both faces. The mylar cathodes act also as gas windows and are metallized only on the internal face. Since the anode is in between the two cathodes, its voltage can be kept halved with respect to a geometry with only two electrodes for the same gas gap. The cathodes are azimuthally divided into eight parts in order to follow the 8-sector partition of the RCo in the φ coordinate.

The gas (CF4) used is the same as in GARFIELD’s drift chambers.

Behind each IC sector is placed a trapezoidal 300 µm thick Silicon (nTD) pad. These pads are segmented into eight strips increasing the detector’s granularity (Figure 2.6) up

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Strip Int. radius (mm) Ext. radius (mm) Min. angle (deg) Max. angle (deg)

1 77.9 85.0 15.6 17.0 2 70.8 77.8 14.2 15.6 3 63.7 70.7 12.9 14.2 4 56.6 63.6 11.5 12.8 5 49.4 56.4 10.1 11.4 6 42.3 49.3 8.6 10.0 7 35.2 42.2 7.2 8.6 8 26.2 35.1 5.4 7.2

Table 2.2: Radii and polar angle limits of RCo silicon strips.

to ∆θ ≈ ±0.7° for the polar angle. The use of silicon detectors allows to obtain an energy resolution of around 0.3%. They are reverse mounted, namely oriented in such a way that the particles impinge on the ohmic side. This mounting has been studied by the FAZIA group and proved to increase the fragment discrimination capabilities by means of PSA [37] as it will be discussed in 3.2.3. In Table 2.2 above are listed the radii and angles covered by each of the 8 strips. The overall geometrical coverage of the Si stage is about 90%. The remaining inactive area is due to the interstrip regions, containing the guard rings, and to the printed circuit board frame that holds each Si sector.

Finally, for each sector, there are 6 CsI(Tl) crystals read by a photodiode (model S2744-08 manufactured by Hamamatsu) with active area 10 mm x 18 mm. These crys-tals are similar to those employed in GARFIELD but they have a different percentage

Figure 2.5: Picture of the Ring Counter detector and the electronic counterpart con-nected to this detector.

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Figure 2.6: The Ring Counter’s silicon strips (left) and the superposition (right) with the corrisponding Cesium crystals.

of thallium doping (between 1500 and 2000 ppm) as to enhance their light output. Alto-gether, we have 48 Cesium Iodide crystals, each one covering half sector in the azimuthal coordinate. As a result of the mentioned division in sectors, an accuracy of 22.5° is obtained in the azimuthal angle of the particles impinging on the scintillators. These CsI(Tl) crystals can also reach an overall 2-3% energy resolution. The designed overlap between Silicon pads and CsI(Tl) crystals is illustrated in Figure 2.6 and it can be seen that at least two Silicon strips correspond to each crystal.

2.3 Electronics

The various detectors, except for the GARFIELD drift chamber, are equipped with digital electronic processing stages. Each signal, from all the detectors, is processed by charge sensitive preamplifiers with different gain. These preamplifiers are located inside the scattering chamber to reduce noise influence upon the already small signals generated. Subsequently, the outputs of the preamplifiers are feed into digital cards developed within the collaboration by the Florence group. These cards contain a 125 MHz, 12 bit ADC (Analog-to-Digital Converter ) and a DSP (Digital Signal Processor ). The DSP is programmable and it is capable of performing advanced on-line data

reduction [38]. This means that instead of sending all the digitized samples to the

acquisition, the DSP elaborates the data and reduces them by applying filtering and shaping algorithms. According to the different detector type a specific calculation is performed and the DSP also extracts information like time and parameters apt to particle identification from the sampled signal. For example, a semi-gaussian digital filter is applied to the signal coming out from every detector; this is particularly useful for

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extracting the maximum amplitude which it is known to be proportional to the energy of the incident particles. However, so as to check the behaviour of the cards, every 1000 events the DSP sends a complete waveform to acquisition for further off-line checks and debugging analysis. In Figure 2.7 the structure diagram of an acquisition channel is shown.

Figure 2.7: Main components of a digital acquisition channel: an analog input stage, the ADC, an internal FIFO (First In First Out ) memory, a trigger section and the DSP.

Signals coming from the microstrip pads, inside GARFIELD’s drift chambers, instead are processed by a usual analog chain which is made of a charge amplifier followed by a peak sensing ADC. A digital upgrade, for the GARFIELD drift chamber, is currently underway in order to have a better position determination from the drift time.

2.3.1 Triggers and Acquisition

As shown in Figure 2.7, the acquisition system contains a section called trigger logic. This results to be fundamental for the experiment as it represents a direct connection with the physics of the reaction. To be more precise, it allows us to impose physical conditions using logical combinations of trigger signals based on the type of reaction mechanism we want to study. If we acquire everything coming from the detectors, most of the data would be useless events mostly dominated by the elastic and quasi-elastic rates.

These selections are made by using two types of triggers, namely local triggers and validation signals. The first ones are generated from a detector signal that has exceeded its acquisition threshold by means of a CFD (Constant Fraction Discrimination). There-fore, it is possible to obtain local triggers from GARFIELD’s CsI(Tl) crystals or from the

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Bit Trigger Reduction Description

0 OR CsI GARF 2 OR of the GARFIELD scintillators

1 OR IC RCo 1 OR of the different parts of IC

2 OR Si RCo 1 OR among the RCo strips

3 OR GARF AND OR Si RCo 1 AND of trigger 0 and trigger 2

4 OR GARF AND OR IC RCo 1 AND of trigger 0 and trigger 1

5 OR Si AND OR IC 1 AND of trigger 2 and trigger 1

6 Plastic Monitor 100 Plastic Scintillator

7 Pulser 1 Pulse Generator

Table 2.3: The available triggers with their reduction factors which include the ones selected during the measurements.

RCo silicon detectors. On the other hand, a validation signal is generated by a trigger box (CAEN V1495), which is a VME standard electronic board, featuring an FPGA (Field Programmable logic array) programmed to perform coincidence and trigger tasks. This trigger box collects all the various local triggers and generates a validation signal according to a user defined table of possible combinations inside a specific time window. When a validation signal occurs, the acquisition starts and the DSP sends its data to be stored on disk.

During the experiment, up to eight different local trigger combinations can be pro-grammed. The trigger-box output is a bitmask that indicates which trigger was acti-vated. In Table 2.3 are reported the different triggers available for this experimental campaign. Each bit is associated with a particular type of trigger. Moreover, often it was used a reduction factor ”R” as to activate the acquisition once every ”R” occur-rences. Throughout this experiment, the triggers selected were trigger 0 and trigger 2 (Table 2.3). These two triggers, are imposed by the light nature of the excited system produced in the reaction and its kinematics, be it a CN or projectile-like fragment. In fact, in the former case one will mainly have an evaporation residue at small angles in RCo and few LCP in GARFIELD. Therefore, we adopted as the main physics trigger the OR of triggers signals coming from the RCo (trigger 2) and the additional OR from the GARFIELD signals (trigger 0). More specifically, trigger 0 is the logic OR of all CsI(Tl) signals while trigger 2 is obtained from the logic OR of Si strip signals. The coincidence (logic AND) between these two triggers (trigger 3), even though non activated, can be recovered during the offline analysis.

Besides the measurement triggers mentioned above, two additional triggers were used. One of them is a pulser trigger (bit 7 in Table 2.3), applied to control the stability of the whole electronic chain. This is especially useful when interested to sum data from several runs of measurement. A pulse generator creates signals with a well known amplitude and stable in time, which can be employed afterwards to correct potential faults due to

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the electronic response. And last, bit 6 is a trigger referred to a plastic scintillator that is positioned at a polar angle (θ '1.2 °) smaller than the grazing angle. This scintillator registers elastic Rutherford scattering events in order to normalize counts to the absolute cross sections.

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Chapter 3 The Experimental Measurement and

Energy Calibration

In the first part of this chapter, the experimental conditions of the reactions measure-ment are introduced. Then we will proceed by describing the methods used to identify the particles detected with the GARFIELD + RCo apparatus.

These methods, as mentioned in Chapter 2, are the ∆E-E and the Pulse Shape tech-niques for particles detected with Cesium Iodide scintillators. Furthermore, since the RCo detector is equipped with a silicon detection stage it is also possible to make use of a Pulse Shape technique, consisting in an energy-rise time correlation to identify parti-cles. Another section will be dedicated to the energy calibration process of the apparatus, mainly through the elastically scattered Oxygen ejectiles by a 197_{Au target, measured}

between the different runs of the experiment. This allows to calibrate in energy the response of the silicon detector and therefore to reconstruct the energy of the incident particles impinging on a detector. Finally, we will present a few global observables able to select the particular reaction mechanisms of interest.

3.1 The Measurement

The measurements were performed using a pulsed beam (1 ns resolution and 400

ns repetition period) of 16_{O with an energy of 90.5, 110 and 130 MeV supplied by}

the Tandem XTU accelerator at the INFN laboratories in Legnaro. This electrostatic accelerator is based on two acceleration stages, as it is shown by the operational sketch

in Figure 3.1. Ions are generated inside an external source and are extracted with

a weakly positive charge state (q=+1). Before entering in Tandem, the ions cross a charge-exchange region filled with gas (Cesium) in which, by playing on the relative electronic affinity, there is a high probability of receiving two electrons from the gas. With such charge state (q=-1), the ions enter the low energy side of the tandem and are

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CHAPTER 3. THE EXPERIMENTAL MEASUREMENT AND ENERGY CALIBRATION

Figure 3.1: Illustration of a Tandem accelerator were the following elements can be identified: the accelerating pipe, the column which supports the high voltage terminal, the ”stripping” chamber, the ”ladderton” charging belt and last the bending magnets .

attracted towards a high voltage terminal (HVT) at +14.5 MV, located in the centre of the accelerator. Inside the terminal (a Faraday cage), the ions pass through a very thin carbon foil called ”stripper”. As the name suggests, this device can strip a large number of electrons to the ions (up to q=10-20 depending on the ion type and the acquired energy). The ions then enter the opposite side of the HVT with a highly positive charge state. The repulsive electrostatic field then accelerates furthermore the ions in the second half of the accelerator. Afterwards, the exiting particles are driven, using magnetic deflectors and lenses, towards the measurement apparatus where the target is located.

The 16_{O generated beam, in our case having a maximum intensity of about 0.1 pnA,}

impinges on 12C self-supporting target with a thickness of 85 µg/cm2. In the case of complete fusion, for the three beam energies (90.5, 110 and 130 MeV ), such reaction leads to a fused 28_{Si system respectively at 55, 63 and 72 MeV excitation energy. The trigger}

configuration, described in section 2.3.1, focuses on the selection of a fused system (CN). Nevertheless, it is sufficiently flexible to allow studying peripherical events as well. An automatic system was available for changing target operations in order to swap between the slots containing the carbon foils and therefore avoid wear off the target. Under the same beam conditions, the16_O+197_{Au reaction was measured providing a reference point}

for the energy calibration by means of the elastically scattered 16_{O ions. Together with}

the Gold and Carbon foils, an additional AlO2 target was present in the target holder.

Its purpose is to allow for the initial beam focalization. Indeed this material is lighten when hit by the beam. A central hole allows to position the beam on the center of the

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CHAPTER 3. THE EXPERIMENTAL MEASUREMENT AND ENERGY CALIBRATION

target, also by maintaining the alignment with two other AlO2 foils positioned at the

beginning and at the end of the scattering chamber, and to control its size to about 1mm in diameter .

Figure 3.2: Countings for the complete apparatus (GARFIELD + RCo) on the left and for the Ring counter on the right. The figure for RCo is a zoom of the internal crown present on the left. As it can be seen, four GARFIELD detectors are not counting due to bad functioning.

An online control of the acquired data during the measurement sessions was possible due to a graphical interface program named GARFIELD Monitor [39]. This ROOT-based software can visualize several pre-defined 1D and 2D histograms, filled either with raw experimental data or with preprocessed variables. For example, one can have an overall view of the operation of the apparatus by plotting the countings for each separate detector within the apparatus (see Figure 3.2). The GARFIELD Monitor is crucial during the first phase of the measurement as it allows the setting of ADC pedestals and software thresholds. Another parameter kept under close control was the dead time because in this time window the system is inhibited due to the time needed to process the signal. As a consequnce, all new events are lost causing an inefficiency in the counting rate. The dead time, throughout which the acquisition system collects the data, has been limited to around 30%-50% by adjusting the beam intensity. The acquisition system is able to measure the dead time by counting all the signals that can be processed over the total number of events hitting the detectors.

To verify the electronic stability of the pre-amplification, from time to time a pulser run is acquired. The pulser is a signal generator that produces pulses similar to the ones generated by the detectors. In this way, one can test the stability and linearity of the gain which may be sensitive to environmental conditions such as temperature variations.

The 16O+ 12C reaction at 90.5, 110 and 130 MeV beam energy

Alma Mater Studiorum · Universit`

a di Bologna

The

16

O+

12

C reaction at 90.5, 110 and 130

MeV beam energy

Relatore:

Prof. Mauro Bruno

Correlatore:

Dott. Luca Morelli

Presentata da:

Catalin Frosin

Sessione III

Contents

Abstract

Introduction

Chapter 1

The Physics Case

1.1

Introduction to Heavy Ion Collisions

1.1.1

Peripheral and Direct Reaction

1.1.2

Central Collisions and Compound Nucleus

1.2

Statistical Decay

1.3

Structure and Clustering Effects

1.3.1

The

O nucleus

1.4

The

O+

C Reaction

Chapter 2

The Experimental Apparatus

2.1

GARFIELD Apparatus

2.1.1

Drift Chamber and Microstrip

2.1.2

CsI(Tl) Crystals

2.2

Ring Counter

2.3

Electronics

2.3.1

Triggers and Acquisition

Chapter 3

The Experimental Measurement and

Energy Calibration

3.1

The Measurement